A control system featuring a double pole at the origin is unstable because its corresponding time-domain response term________________?
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Answer: C. Grows linearly with time
Explanation
A double pole at the origin in a transfer function contributes a ramp term in the time domain. Mathematical inverse Laplace transforms convert a squared s term into linear time dependence. This unconstrained growth causes the system response to increase linearly without bound over time. Poles located in the right half-plane or multiple poles at the origin indicate instability. Control system stability requires all closed-loop poles to reside in the left half-plane. Time-domain responses determine whether system outputs decay, stabilize, or grow indefinitely.
Control engineers design feedback loops to relocate poles and ensure closed-loop system stability. Unstable controllers that grow linearly with time will quickly saturate final control elements. Preventing double poles at the origin is a fundamental rule in industrial control design. A constant time-domain response requires poles with zero growth factors rather than origin poles. Exponential growth is typically caused by poles located in the right half of the complex plane. Decaying linearly with time contradicts the increasing magnitude produced by multiple origin poles.
- Subject
- Engineering
- Category
- Chemical Engineering
- Topic
- —
- Difficulty
- medium
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